Mathematical Research Letters

Volume 15 (2008)

Number 6

Spectrum of the Laplacian on manifolds with Spin(9) holonomy

Pages: 1167 – 1186

DOI: http://dx.doi.org/10.4310/MRL.2008.v15.n6.a8

Author

Kwan-hang Lam (National Cheng Kung University)

Abstract

We consider noncompact complete manifolds with Spin(9) holonomy and proved an one end result and a splitting type theorem under different conditions on the bottom of the spectrum. We proved that any harmonic functions with finite Dirichlet integral must be Cayley-harmonic, which allowed us to conclude an one end result. In the second part, we established a splitting type theorem by utilizing the Busemann function.

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